Example 4 :
Find the roots of the equation x-
1
3x
=
1
6
(x ¹ 0)
Solution :
We have x-
1
3x
=
1
6
Þ 6x
2
- x - 2 = 0
6x
2
– x – 2 = 6x
2
+ 3x – 4x – 2
= 3x (2x + 1) – 2 (2x + 1)
= (3x – 2)(2x + 1)
The roots of 6x
2
– x – 2 = 0 are the values of x for which (3x – 2)(2x + 1) = 0
Therefore, 3x – 2 = 0 or 2x + 1 = 0,
i.e., x =
2
3
or x =
1
2
-
Therefore, the roots of 6x
2
– x – 2 = 0 are
2
3
and
1
2
- .
We verify the roots, by checking that
2
3
and
1
2
- satisfy 6x
2
– x – 2 = 0.
Example-5.
Find the width of the space for spectators discussed in section 5.1.
Solution :
In Section 5.1, we found that if the width of the space for spectators is x m, then x
satisfies the equation 2x
2
+ 45x - 47 = 0.
Applying the factorisation method we write this equation
as:-
2x
2
- 2x + 47x - 47 = 0
2x (x - 1) + 47 (x - 1) = 0
i.e., (x - 1) (2x + 47) = 0
So, the roots of the given equation are x = 1 or x =
47
2
-
.
Since ‘x’ is the width of space
of the spectators it cannot be negative.
Thus, the width is 1 m. So it is not enough for spectators.
EXERCISE - 5.2
1. Find the roots of the following quadratic equations by factorisation:
i. x
2
– 3x – 10 = 0
ii. 2x
2
+ x – 6 = 0
iii. 2
2 7 52 0 x x ++ =
iv. 2 1
2 0
8
x x -+ =
v. 100x
2
– 20x + 1 = 0
vi. x(x + 4) = 12
vii. 3x
2
– 5x + 2 = 0
viii.
3
x - = 2
x
(x ¹ 0)
ix. 3(x – 4)2
– 5
page no:112
Home